Optimal convergence of a discontinuous-Galerkin-based immersed
 boundary method*

Adrian J. Lew; Matteo Negri

Displaying similar documents to “Optimal convergence of a discontinuous-Galerkin-based immersed boundary method*”

Optimal convergence of a discontinuous-Galerkin-based immersed boundary method

Adrian J. Lew, Matteo Negri (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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We prove the optimal convergence of a discontinuous-Galerkin-based immersed boundary method introduced earlier [Lew and Buscaglia, (2008) 427–454]. By switching to a discontinuous Galerkin discretization near the boundary, this method overcomes the suboptimal convergence rate that may arise in immersed boundary methods when strongly imposing essential boundary conditions. We consider a model Poisson's problem with homogeneous boundary conditions over two-dimensional...

error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ...

High-frequency limit of the Maxwell-Landau-Lifshitz equations in the diffractive optics regime

LU Yong (2012)

ESAIM: Proceedings

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We study the Maxwell-Landau-Lifshitz system for highly oscillating initial data, with characteristic frequencies (1 ) and amplitude (1), over long time intervals (1 ), in the limit → 0. We show that a nonlinear Schrödinger equation gives a good approximation for the envelope of the solution in the time interval under consideration. This extends previous results of Colin and Lannes [1]. This text is a short version of the article [5].

A posteriori error analysis for the Crank-Nicolson method for linear Schrödinger equations

Irene Kyza (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We prove error estimates of optimal order for linear Schrödinger-type equations in the ( )- and the ( )-norm. We discretize only in time by the Crank-Nicolson method. The direct use of the reconstruction technique, as it has been proposed by Akrivis in [ 75 (2006) 511–531], leads to upper bounds that are of optimal order in the ( )-norm, but of suboptimal order in the ( ...

Local semiconvexity of Kantorovich potentials on non-compact manifolds

Alessio Figalli, Nicola Gigli (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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We prove that any Kantorovich potential for the cost function = /2 on a Riemannian manifold (, ) is locally semiconvex in the “region of interest”, without any compactness assumption on , nor any assumption on its curvature. Such a region of interest is of full -measure as soon as the starting measure does not charge – 1-dimensional rectifiable sets.

Robust operator estimates and the application to substructuring methods for first-order systems

Christian Wieners, Barbara Wohlmuth (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We discuss a family of discontinuous Petrov–Galerkin (DPG) schemes for quite general partial differential operators. The starting point of our analysis is the DPG method introduced by [Demkowicz , 49 (2011) 1788–1809; Zitelli , 230 (2011) 2406–2432]. This discretization results in a sparse positive definite linear algebraic system which can be obtained from a saddle point problem by an element-wise Schur complement reduction applied to the test space. Here, we show that the abstract...